1. Phase Diagrams

2. What is Phase?
The term ‘phase’ refers to a separate and identifiable state of matter in which a given substance may exist.
Applicable to both crystalline and non-crystalline materials
An important refractory oxide silica is able to exist as three crystalline phases, quartz, tridymite and cristobalite, as well as a non-crystalline phase, silica glass, and as molten silica
Every pure material is considered to be a phase, so also is every solid, liquid, and gaseous solution
For example, the sugar–water syrup solution is one phase, and solid sugar is another
2. its use provides a convenient way of expressing a material’s structure ….
3. Quartz -> a hard glossy mineral consisting of silicon dioxide in crystal form; Tridymite -> Tridymite is a high-temperature polymorph of quartz and usually occurs as minute tabular white or colorless pseudo-hexagonal triclinic crystals; Cristobalite -> a white mineral consisting of silica; found in volcanic rocks

3. Introduction to Phase Diagram
There is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its phase diagram
It is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium
Provides valuable information about melting, casting, crystallization, and other phenomena
1. The understanding of phase diagrams for alloy systems is extremely important because …

4. ISSUES TO ADDRESS... • When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
--a composition (e.g., wt% Cu - wt% Ni), and
--a temperature (T )
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
Cupronickel alloy (55% Cu and 45% Ni)
Phase B
Phase A
Nickel atom
Copper atom

5. Solubility Limit
At some specific temperature, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution, which is called as Solubility Limit
The addition of solute in excess of this solubility limit results in the formation of another compound that has a distinctly different composition
This solubility limit depends on the temperature
2. consider the sugar– water ( ) system. Initially, as sugar is added to water, a sugar–water solution or syrup forms. As more sugar is introduced, the solution becomes more concentrated, until the solubility limit is reached, or the solution becomes saturated with sugar. At this time the solution is not capable of dissolving any more sugar, and further additions simply settle to the bottom of the container. Thus, the system now consists of two separate substances: a sugar–water syrup liquid solution and solid crystals of undissolved sugar

6. Solubility Limit Sugar-Water

7. Microstructure
the structure of a prepared surface of material as revealed by a microscope above 25× magnification
The microstructure of a material can strongly influence properties such as strength, toughness, ductility, hardness, corrosion resistance, high/low temperature behavior, wear resistance, etc
After appropriate polishing and etching, the different phases may be distinguished by their appearance /
Figure -> SEM of plain carbon (0.45%) steel. The large dark areas are proeutectoid ferrite. Regions having the alternating light and dark lamellar structure are pearlite; the dark and light layers in the pearlite correspond, respectively, to ferrite and cementite phases.

8. Components and Phases • Components: • Phases: b (lighter phase) a
The elements or compounds which are present in the mixture
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., a and b).
Aluminum-
Copper
Alloy b
(lighter
phase) a
(darker
phase)

9. Effect of T & Composition (Co)
• Changing T can change # of phases:
path A to B.
Changing Co can change # of phases:
path B to D.
B (100°C,70)
1 phase
D (100°C,90)
2 phases 70 80
100 60 40 20
Temperature (°C) Co
=Composition (wt% sugar) L (
liquid solution
i.e., syrup)
(liquid) + S
(solid
sugar)
water-
sugar
system
A (20°C,70)
2 phases

10. PHASE EQUILIBRIA
Free Energy -> a function of the internal energy of a system, and also the disorder of the atoms or molecules (or entropy)
A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition
A change in temperature, pressure, and/or composition for a system in equilibrium will result in an increase in the free energy
And in a possible spontaneous change to another state whereby the free energy is lowered
0. Equilibrium is another essential concept that is best described in terms of a thermodynamic quantity called the free energy
2. In a macroscopic sense, this means that the characteristics of the system do not change with time but persist indefinitely; that is, the system is stable

11. Unary Phase Diagram
Three externally controllable parameters that will affect phase structure: temperature, pressure, and composition
The simplest type of phase diagram to understand is that for a one-component system, in which composition is held constant
Pure water exists in three phases: solid, liquid and vapor
0. Also called as one-component phase diagram
2. (i.e., the phase diagram is for a pure substance); this means that pressure and temperature are the variables.

12. Pressure-Temperature Diagram (Water)
Each of the phases will exist under equilibrium conditions over the temperature–pressure ranges of its corresponding area
The three curves (aO, bO, and cO) are phase boundaries; at any point on one of these curves, the two phases on either side of the curve are in equilibrium with one another
Point on a P–T phase diagram where three phases are in equilibrium, is called a triple point
2. That is, equilibrium between solid and vapor phases is along curve aO—likewise for the solid-liquid, curve bO, and the liquid-vapor, curve cO
3. all three of the phase boundary curves intersect at a common point, which is labeled O

13. Binary Phase Diagrams
A phase diagram in which temperature and composition are variable parameters, and pressure is held constant—normally 1atm
Binary phase diagrams are maps that represent the relationships between temperature and the compositions and quantities of phases at equilibrium, which influence the microstructure of an alloy.
Many microstructures develop from phase transformations, the changes that occur when the temperature is altered
… we will concern ourselves with binary alloys—those that contain two components. If more than two components are present, phase diagrams become extremely complicated and difficult to represent. .
Binary phase diagrams are helpful in predicting phase transformations and the resulting microstructures, which may have equilibrium or nonequilibrium character.

14. Phase Equilibria Simple solution system (e.g., Ni-Cu solution) Crystal
Structure
electroneg
r (nm) Ni
FCC
1.9
0.1246 Cu
1.8
0.1278
Micsible -> capable of being mixed
Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility.
Ni and Cu are totally miscible in all proportions.

15. Phase Diagrams • Indicate phases as function of T, Compos, and Press.
• For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
• 2 phases: L
(liquid) a
(FCC solid solution)
• 3 phase fields:
L +
wt% Ni 20 40 60 80
100
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
(FCC solid
solution) +
liquidus
solidus
• Phase
Diagram
for Cu-Ni
system

16. Phase Diagrams: # and types of phases
• Rule 1: If we know T and Co, then we know:
--the number and types of phases present.
wt% Ni 20 40 60 80
100
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid) a
(FCC solid
solution) L +
liquidus
solidus
Cu-Ni
phase
diagram
• Examples:
A(1100°C, 60):
1 phase: a B
(1250°C,35) B
(1250°C, 35):
2 phases: L + a
A(1100°C,60)

17. Phase Diagrams: composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 30 40 50
Cu-Ni system
• Examples: T A C o
= 35 wt% Ni
tie line 35 C o
At T A
= 1320°C:
Only Liquid (L) C L
= C o
( = 35 wt% Ni) B T 32 C L 4 C a 3
At T D
= 1190°C: D T
Only Solid ( a ) C
= C o
( = 35 wt% Ni
Last 2 points -> Melting point of Ni is more than Cu, it means that solidus phase will consist of more percentage of Ni as compared to that in liquidus phase
At T B
= 1250°C:
Both a
and L C L
= C
liquidus
( = 32 wt% Ni here) C a
= C
solidus
( = 43 wt% Ni here)

18. Phase Diagrams: weight fractions of phases
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5
Cu-Ni system T A 35 C o 32 B D
tie line R S
• Examples: C o
= 35 wt% Ni
At T A
: Only Liquid (L) W L
= 100 wt%, W a
= 0
At T D :
Only Solid ( a ) W L
= 0, W
= 100 wt%
At T B :
Both a
and L
= 27 wt% WL = S R + Wa

19. The Lever Rule
Tie line – connects the phases in equilibrium with each other - essentially an isotherm
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5 B T
tie line C o S R
How much of each phase? Think of it as a lever (teeter-totter) ML M R S
M -> Mass; C0 -> original composition

20. Ex: Cooling in a Cu-Ni Binary
• Phase diagram:
Cu-Ni system.
wt% Ni 20
120
130 3 4 5
110
L (liquid) a
(solid) L +
T(°C) A 35 C o
L: 35wt%Ni
Cu-Ni
system
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100 wt% Ni.
a: 46 wt% Ni
L: 35 wt% Ni B 46 35 C 43 32 a :
43 wt% Ni
L: 32 wt% Ni D 24 36
L: 24 wt% Ni a :
36 wt% Ni E
• Consider
Co = 35 wt%Ni.

21. Cored vs Equilibrium Phases
• Ca changes as we solidify.
• Cu-Ni case:
First a to solidify has Ca = 46 wt% Ni.
Last a to solidify has Ca = 35 wt% Ni.
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
First a
to solidify:
46 wt% Ni
Uniform C :
35 wt% Ni
Last
< 35 wt% Ni
Bottom-middle figure is the microstructure just before solidifying completely

22. Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS)
--Ductility (%EL,%AR)
Tensile Strength (MPa)
Composition, wt% Ni Cu Ni 20 40 60 80
100
200
300
400
TS for
pure Ni
TS for pure Cu
Elongation (%EL)
Composition, wt% Ni Cu Ni 20 40 60 80
100 30 50
%EL
for
pure Ni
for pure Cu
--Peak as a function of Co
--Min. as a function of Co

23. Eutectic System
A eutectic system is a mixture of chemical compounds or elements that has a single chemical composition that solidifies at a lower temperature than any other composition

24. Binary-Eutectic Systems
has a special composition
with a min. melting T.
2 components
Cu-Ag
system
T(°C)
Ex.: Cu-Ag system
1200
• 3 single phase regions
L (liquid)
(L,
a, b )
1000 a
• Limited solubility: a L + L + b
800
779°C b a TE
: mostly Cu
8.0
71.9
91.2 b
: mostly Ag
600
• TE
: No liquid below TE a + b
The α phase is a solid solution rich in copper; it has silver as the solute component and an FCC crystal structure. The β-phase solid solution also has an FCC structure, but copper is the solute
• CE
: Min. melting TE
400
composition
200 20 40 60 CE 80
100
• Eutectic transition
L(CE) (CE) + (CE) Co ,
wt% Ag

25. EX: Pb-Sn Eutectic System (1)
• For a 40 wt% Sn - 60 wt% Pb alloy at 150°C, find...
--the phases present:
a + b
Pb-Sn
system
--compositions of phases: L + a b
200
T(°C)
18.3
C, wt% Sn 20 60 80
100
300
L (liquid)
183°C
61.9
97.8
CO = 40 wt% Sn
Ca = 11 wt% Sn
Cb = 99 wt% Sn
--the relative amount of each phase: W a =
C - CO
C - C 59 88
= 67 wt% S
R+S
150 R 11 C 40 Co S 99 C
Sn -> Tin W  =
CO - C
C - C R
R+S 29 88
= 33 wt%

26. EX: Pb-Sn Eutectic System (2)
• For a 40 wt% Sn - 60 wt% Pb alloy at 220°C, find...
--the phases present:
a + L
Pb-Sn
system
--compositions of phases: L + b a
200
T(°C)
C, wt% Sn 20 60 80
100
300
L (liquid)
183°C
CO = 40 wt% Sn
Ca = 17 wt% Sn
CL = 46 wt% Sn
--the relative amount of each phase:
220 17 C R 40 Co S 46 CL W a =
CL - CO
CL - C 6 29
= 21 wt% W L =
CO - C
CL - C 23 29
= 79 wt%

27. Microstructures in Eutectic Systems: I
• Co < 2 wt% Sn
• Result:
--at extreme ends
--polycrystal of a grains
i.e., only one solid phase. L + a
200
T(°C) Co ,
wt% Sn 10 2 20
300
100 30 b
400
(room T solubility limit) TE
(Pb-Sn
System)
L: Co wt% Sn a L
a: Co wt% Sn
Last -> There will be no beta

28. Microstructures in Eutectic Systems: II
L: Co wt% Sn
• 2 wt% Sn < Co < 18.3 wt% Sn
• Result:
Initially liquid + 
then  alone
finally two phases
a polycrystal
fine -phase inclusions
Pb-Sn
system L + a
200
T(°C) Co ,
wt% Sn 10
18.3 20
300
100 30 b
400
(sol. limit at TE) TE 2
(sol. limit at T
room ) L a
a: Co wt% Sn a b

29. Microstructures in Eutectic Systems: III
• Co = CE
• Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of a and b crystals.
160 m
Micrograph of Pb-Sn
eutectic
microstructure
Pb-Sn
system
L
a
200
T(°C)
C, wt% Sn 20 60 80
100
300 L a b +
183°C 40 TE
L: Co wt% Sn CE
61.9
18.3
: 18.3 wt%Sn
97.8
: 97.8 wt% Sn

30. Lamellar Eutectic Structure

31. Microstructures in Eutectic Systems (Pb-Sn): IV
• wt% Sn < Co < 61.9 wt% Sn
• Result: a crystals and a eutectic microstructure WL
= (1- W a )
= 50 wt% C
= 18.3 wt% Sn CL
= 61.9 wt% Sn S R + =
• Just above TE :
Pb-Sn
system L + b
200
T(°C)
Co, wt% Sn 20 60 80
100
300 a 40 TE
L: Co
wt% Sn L a L a
18.3
61.9 S R
97.8 S R
primary a
eutectic b
Second last S = 97.8 – 40 = 57.8
• Just below TE : C a
= 18.3 wt% Sn b
= 97.8 wt% Sn S R + W =
= 73 wt%
= 27 wt%

32. Hypoeutectic & Hypereutectic
300 L
T(°C) L + a a b
200 L + b
(Pb-Sn TE
System) a + b
100
175 mm a
hypoeutectic: Co = 50 wt% Sn
hypereutectic: (illustration only) b
Co, wt% Sn 20 40 60 80
100
eutectic
61.9
eutectic: Co = 61.9 wt% Sn
When the composition of an alloy places it to the left of the eutectic point it is called hypo-eutectic. Note, though, that this is merely convention. If the phase diagram had been drawn the other way around, with 100%A on the right and 100%B on the left, then the same alloy would be called hyper-eutectic, as it would be to the right of the eutectic point
When the composition of an alloy places it to the right of the eutectic point it is called hyper-eutectic
Left most figure -> Alpha grains are the primary grains that were formed during the phase (Liquid + Alpha), i.e. formed before crossing eutectic isotherm. The other lamellar structure is eutectic alpha + eutectic beta
160 mm
eutectic micro-constituent